wailing vs wailful

wailing is a noun but wailful is not a noun.

Word	Noun	Adjective	Verb	Adverb
wailing	Yes	Yes	No	No
wailful	No	Yes	No	No

As adjectives, wailing and wailful are synonyms defined as:

wailing and wailful: vocally expressing grief or sorrow or resembling such expression

Other synonyms of wailing include lamenting.

wailing (noun)	wailful (noun)
loud cries made while weeping

wailing (adjective)	wailful (adjective)
vocally expressing grief or sorrow or resembling such expression	vocally expressing grief or sorrow or resembling such expression